numerical modelling of rock anchor pullout and the influence of discrete fracture networks on the

144 Pages·2014·13.8 MB·English

NUMERICAL MODELLING OF ROCK ANCHOR PULLOUT AND THE INFLUENCE OF DISCRETE
FRACTURE NETWORKS ON THE CAPACITY OF FOUNDATION TIEDOWN ANCHORS

by

BRAD PANTON

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE

in

THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES
(Mining Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA
(Vancouver)

April 2016

©Brad Panton, 2016
ABSTRACT
Numerous studies presented in this thesis have reported failure of the rock mass surrounding an
anchor, as a result of applied external tensile loads (i.e. pullout loads) transferred to rock mass from
the anchor and the overlying structure. Resistance to this failure mechanism is provided in design
by assuming that the dead weight of a uniformly shaped inverted “cone”, with an assumed initiation
point and breakout angle, provides resistance to the design loads. In some cases, a minor
contribution of rock mass tensile or shear strength is considered by designers across the area of the
assumed pullout cone. Strength estimates for this additional resistance are based primarily on
sparse historic testing data, rock mass rating type relationships developed for other applications,
and engineering judgement. However, rock mass rating systems assume that the rock mass is
homogenous and isotropic, and at the scale of the anchor this assumption may not be valid since
individual fractures may influence anchor stability.
As an alternative to the current foundation anchor design method, this research presents a new
approach to the rock cone pullout problem using Discrete Fracture Networks (DFN) combined with
numerical simulations. The simulations presented in the research investigate the influence of
fractures in a synthetic rock mass on ultimate anchor strength, with the purpose of developing a
method for incorporation of scale effects of jointing in anchor design.
By using numerical simulations that allow the load transfer mechanism from the anchor to the rock
mass to vary with stiffness, it is contended that the failure mechanism of the rock mass under the
applied loading can be considered more appropriately in anchor designs. It is also contended that
some aleatory variability associated with fractures can be quantified using a DFN-based approach.
Fractures are observed to have an influence on both the load distribution in the anchor as well as
the ultimate resistance of the rock mass to pullout. The mapping considerations required to
produce a DFN model for anchor pullout are described in this thesis and recommendations for
i ncorporating DFN based models in anchor design are provided herein.

ii
PREFACE
This thesis is original and independent work done by the author. The author was the lead author in
the one published journal manuscript and two published conference papers based on the work for
this thesis. InN audmdeitriiocnal, thSiem tuhleastiiso snu poef rRvioscokr cCoo-naeu tPhuolrleodu ta lal onfd t hthesee Ipnaflpueernsc lei stoefd D bieslcorwet.e Fracture
Network Statistics on Foundation Anchor Capacity
The paper “
th
”, published in the proceedings of the 13
InternationaDl eISsiRgMn Cofo nRgorceks sF o2u0n1d5a itnio Mn oAnntcrheoarl,a Qguee Ubseicn gis Dbaisscerde toen F Crahcatputreer N5 eintw thorisk sthesis.
The paper “ ”, published in
the inaugural proceedings of the 2014 International Discrete Fracture Network Engineering
Conference iAn VDaisnccroeutev eFrr,a Ccatnuraed aN iest bwaosrekd A opnp Crohaacphte fro 8r itnh et hDise sthigens ios.f Rock Foundation Anchorage
The paper “ ”,
published in the Mining Technology Journal (in press) is based on Chapter 5, 6, and 8 in this thesis.
iii
TABLE OF CONTENTS

Abstract............................................................................................................................................................................. ii
Preface............................................................................................................................................................................... iii
Table of Contents........................................................................................................................................................... iv
List of Tables................................................................................................................................................................... vi
List of Figures..................................................................................................................................................................vii
Acknowledgements...................................................................................................................................................... x

1 Introduction..................................................................................................................................................... 1
1.1 Problem Statement...................................................................................................................... 1
1.2 Research Objectives..................................................................................................................... 2
1.3 Thesis Organization......................................................................................................................3

2 Literature Review......................................................................................................................................... 4
2.1 Introduction..................................................................................................................................... 4
2.2 Canadian Standard of Practice for Anchor Design......................................................... 9
2.3 Full Scale Anchor Pullout Testing…………………………...................................................... 18

3 Using the Discrete Fracture Network Approach in Engineering Design.............................. 24
3.1 General.............................................................................................................................................. 24
3.2 Mapping Requirements............................................................................................................. 25
3.3 Incorporation of DFN’s in Numerical Models………………………………...................... 26

4 Modelling and Calibration of In-elastic Yielding in Jointed Rock............................................. 28
4.1 Introduction……………………………………….............................................................................. 28
4.2 Calibration of Numerical Models............................................................................................ 30
4.2.1 Developing a Sense of Scale From the Canadian Standard of Practice.. 30
4.2.2 Model Setup and Calibration of Phase2 Finite Element Code................... 33

5 Influence of Fractures on Modelled Anchor Capacity................................................................... 39
5.1 Introduction.................................................................................................................................... 39
5.2 Variation in Anchor Capacity for Similar DFN Statistics……………........................... 40
5.3 Influence of Joint Persistence………………………………………........................................... 41
5.4 Influence of Joint Orientation.................................................................................................. 43
5.5 Quantifying Rock Mass Damage (D21).…………………………........................................... 46
5.4 Influence of Confinement on Pullout Capacity and Dilation…................................... 52
5.5 Concluding Remarks and Discussion…………………………………...…............................. 55

6 FEM-DEM Simulation of Fracture Propagation in Intact Rock…………………………….......... 58
6.1 Introduction………………………………………............................................................................. 58
6.2 ELFEN FEM-DEM Model Setup ……………………………….................................................. 58
6.2.1 Description of ELFEN Model and Mechanical Properties of Rock…….... 58
6.2.2 Mechanical Properties of Grout, Steel and Load Setup…….......................... 60
6.3 Load Transfer Mechanism (Elastic and In-Elastic Rock Mass Deformation)….. 61
6.4 Results – Crack Initiation, Propagation and Observed Failure Mechanism……. 64
6.5 Discussion and Summary........................................................................................................... 72

iv
7 Three-Dimensional Analyses……............................................................................................................ 75
7.1 Fracman Analysis of Removable Blocks.............................................................................. 75
7.2 Discussing the Challenges with 3D Simulation of Anchor Pullout........................... 81
7.3 Comments on Up-scaling Numerical Models in 3 Dimensions.................................. 92
8 Foundation Engineering Analysis and Applications..................................................................... 96
8.1 Incorporating the Combined DFN-Numerical Approach into Design................... 96
8.1.1 Comparing to the “Dead Weight Cone” Assumption…………………..…...... 96
8.1.2 Comparing to the “Equivalent Cone Strength” Assumption………..…...... 102
8.1.3 Choosing an Appropriate Numerical Model for a Project………..….......... 105
8.2 Assessing the Load Transfer Mechanism for Post-Tensioned Anchors…............ 107
8.2.1 Calibration Using a 10m Embedment Fully Grouted Dowel ………..….... 107
8.2.2 The Important Consideration of In-Situ Stresses in Calibration............. 108
8.2.3 Designing the Free Stressing Length and Verification................................. 110
8.2.4 Group Effect and Confining Influence of Overlying Structure.................. 113
8.3 Incorporation of Reliability in the Assessment of a Foundation………..…............ 114
8.3.1 Principles of Limit State Design ............................................................................ 114
8.3.2 Ultimate Limit State Analysis Using DFN Based Methods.......................... 116
8.3.3 Discussion on Anchor Serviceability Limit State and Damage................. 120
9 Conclusions and Recommendations.................................................................................................... 121
9.1 Research Conclusions................................................................................................................. 121
9.2 Recommendation for Further Studies................................................................................. 125
References....................................................................................................................................................................... 127
v
List of Tables
Table 1 - Strength parameters used to model anchor pullout…………………………………………………………………….35
Table 2 - Mechanical properties used in ELFEN to assess the influence of the Rotating Crack failure parameters
on the behavior of loaded anchors in massive rock ……………………………………………………………………………………..60
Table 3 - Observed Failure Mechanisms in ELFEN models………………………………………………………………….……….67
Table 4 - Foundation Variability using DFN Sections…………………………………………………………………………………...117
vi
List of Figures
Figure 1 – A Flow Chart Indicating Thesis Structure of Main Research Chapters ................................................................... 3
Figure 2 – A histogram of dams anchored per year (1962-2004) ................................................................................................. 5
Figure 3 – A sketch indicating the number of dams anchored / number of large dams in Canada .................................. 5
Figurλe 4 – A cross section through the spillway block of the historic Catagunya Dam in Tasmania with Anchor
Forces shown (left); and chart indicating anchoring forces plotted against height for a given gradient
(0.8> >0.25) for the downstream face of the dam (right) .............................................................................................................. 6
Figure 5 – A sketch showing the apex angle / breakout angle described by Wyllie for the design of anchors ........ ..11
Figure 6 – Influence of Structural Geology on the Shape of Cones of Rock Mobilized by Uplift Anchors ……………..12
Figure 7 – Conceptual Pier 5 rock foundation design with idealized rock tensile pullout cones ................................ 13
Figure 8 – Idealized group pullout cone geometry estimated based on potential failure along joints
sets developed in the rock mass and pile lengths………………………………………………………………………………………..14
Figure 9– A graphical representation of anchor groups and pullout cones for a small powerhouse…………..........16
Figure 10 – Pullout mechanism described by Weerasinghe and Littlejohn (1997) ........................................................... 17
Figure 11 – A summary of four breakout angle from anchor tests by Saliman and Schaefer 1968……………………18
Figure 12 – Plan view of a full scale pullout test on left, and section view of a full scale pullout failure mechanism
on right, modified after Bruce (1979) .................................................................................................................................................. 19
Figure 13 – Distribution of mapped fracture traces (data source) versus distribution of fracture radius ............... 26
Figure 14 –An example of development of 3D DFN for a large foundation surface ............................................................. 26
Figure 15 –An example of development of 2D cross sections for use in geo-mechanical modelling……………………27
Figure 16 – A comparison of the tensile fracturing in a continuum model (with and without joints) .................... 30
Figure 17 – Theoretical Allowable Anchor Capacity vs. Rock Mass Strength Estimates calculated using the
method recommended by Wyllie, 1999 .............................................................................................................................................. 31
Figure 18 – Axial Stress distribution along Anchor 6 (left) and a plan view sketch indicating the load at which
various fractures in the rock mass surrounding this anchor dilated prior to failure during testing (right) ........... 36
Figure 19 - Dilation of upper rock mass at 0.32 MN load (left); and 0.44 MN load (right) for two different loading
stages of the same finite element model .............................................................................................................................................. 38
Figure 20 - Fracture Intensity vs. Anchor Capacity plots for fracture networks in the 3<P21<6 Range, and, a
comparison of two model realizations for fractures networks in the 3<P21<6 Range (right) ....................................... 41
Figure 21 - Fracture Intensity vs. Ultimate Load plots for 1.0, 0.8 and 0.5 Persistence Factors .................................... 42
Figure 22 - Fracture Intensity vs. Ultimate Load plots for +0, +20 and +45 Orientation Factors……………………..…44
Figure 23 – Lower bound failure realization indicating greater than 5mm displacement at Load = 0.56MN….....46
Figure 24 – Upper bound failure realization indicating less than 1mm displacement at Load = 1.02MN……..……..46
Figure 25 – A revised joint orientation factor = +0 produces failure with greater than 5mm displacement at
Load = 1.02MN for the same fracture network realization as Figure 27…………………………………………………….……47
Figure 26 – A sketch comparing pre-existing fractures to induced fractures in DFN Realization 1………………..…..48
Figure 27 – Induced Damage Intensity vs. Ultimate Load plots for 25 DFN Realizations…………………………………...49
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List of Figures cont’1

Figure 28 – Greater than 5mm dilation observed at failure for lower bound failure load = 0.7MN…………………..50
Figure 29 – Greater than 5mm dilation observed at failure for upper bound failure load = 1.2MN…………………..50
Figure 30 – Comparison of upper bound (right) and lower bound (left) yielding observed in two different DFN
realizations.……………………………………….………………………..........…… ........................................................................................... 51
Figure 31 – Model setup for typical rock anchor pull test on left (Test force=T, Reactionary Forces=R) compared
to historic ISRM recommendation for rock anchor pullout apparatus set up on right……………………………………..53
Figure 32 – Anchor Test Setup Recommendations (modified after ASTM 4435-84) ……………………………………..53
Figure 33 – Idealized pullout test arrangement provides reaction force inside the area of influence of rock mass
dilation.……………………………………….………………………..........…… .................................................................................................. 54
Figure 34 – Idealized pullout test arrangement provides reaction force well outside of area of influence of rock
mass dilation indicated by color contours in the Phase2 realization shown ......................................................................... 54
Figure 35 – A Phase2 model showing 4 different loading for the confined test model……………………………………..55
Figure 36 – Fracture Scheme in ELFEN. (a) Initial state before fracturing, (b) intra-element crack insertion, and
(c) inter-element crack insertion; Modified after Klerck (2000)… ............................................................................................ 59
σ
Figure 37– ELFEN screenshots showing material properties and mesh size used in FEM-DEM simulations..61
1
Figure 38– Principal Stress, , distribution during Elastic loading at Load Step T=2.0sec for Three Different
σ τ
Intact Rock Moduli, E = 5 GPa (left), 15GPa (middle), 50GPa (right) ...................................................................................... 62
σ
1
Figure 39– Principal Stress (left), , and Shear Stress (right), , distribution at 330kN Load Step ....................... 63
1
Figure 40– A different model indicating Principal Stress, , concentration (left) and stress re-distribution
following in-elastic deformation and cracking… .............................................................................................................................. 63
σ
Figure 41– Various failure modes for classification of the cone failure pullout mechanism ........................................ 65
σ
1
Figure 42– Principal Stress (upper), , at 1170kN Load Step of Model 1 .............................................................................. 66
1
Figure 43– Principal Stress (upper) , , at 500kN load step, and Vertical Displacement at 780kN (middle) and
1100kN (Lower) Load Steps of Model 2, comprising a Young’s Modulus, E=1.5GPa rock mass ................................... 68
Figure 44– A comparison between 1425 kN load steps for Model 5b and Model 6............................................................. 69
Figure 45– Observed Variation in Rock Mass Damage with varying Rotating Crack / Rankine Failure Parameters
and Constant Mohr-Coulomb Friction Angle and Cohesion ........................................................................................................ 71
Figure 46– Observed Rock Mass Damage and Dilation at Final Load Steps (1425kN and 715kN) for two models
with varying Rotating Crack / Rankine Failure Parameters and Constant Mohr-Coulomb Parameters ................... 71
Figure 47– Influence of Pre-Existing Joints on the Failure Mechanism observed in ELFEN ........................................... 74
Figure 48 – Fracman Screenshots illustrating fracture traces on the 50m x 200m sample foundation area...76
Figure 49 – A Fracman screenshot showing formation of removable blocks within a foundation area .................... 77
Figure 50 – A comparison between P21 fracture trace distributions for one realization of DFN1 (left-A.1)
compared to that of DFN2 (right – B.1)………….… ............................................................................................................................. 78
Figure 51 – A comparison of the weight of removable wedges for a given apex depth to curves produced based
on recommendations by Littlejohn and Bruce ................................................................................................................................... 79
Figure 52 – A comparison between the distribution of removable blocks for one realization of DFN1 (A.2, A.3)
and one realization from DFN2 (B.2, B.3) ............................................................................................................................................ 81
Figure 53– A 3DEC Screenshots showing numerical analysis of a dam foundation ........................................................ 82
Figure 54– A 3DEC Screenshots indicating the minimum scale required to calibrate the rock anchor pullout
model ................................................................................................................................................................................................................. 84
Figure 55– A 3DEC screenshot indicating interblock dilation induced by anchoring within a larger scale wedge
formed by prominent faults ....................................................................................................................................................................... 84
Figure 56– A 3DEC Screenshot showing interblock fracture patterns with moderately dipping orientations .... 86
viii
List of Figures cont’2

Figure 57– A 3DEC Screenshot showing interblock fracture patterns with subvertical-subhorizontal joint
orientations ..................................................................................................................................................................................................... 86
Figure 58 – An overlay from Bruce (1979) on a plan view screenshot taken from a 3DEC model ................................ 87
Figure 59 – 3DEC screenshots showing the loading block, cable bolt element and grouted volume used to
analyze the cone pullout mechanism .................................................................................................................................................... 88
Figure 60 – 3DEC Screenshots showing maximum deformation and dilation in the rock mass of approximately
1mm in the upper rock mass at maximum loading of 250kN loading in anchor ................................................................. 89
Figure 61 – 3DEC Screenshots showing dilation at 1600MN load with over 5mm interblock deformation
occurring within the maximum probable wedge .............................................................................................................................. 90
Figure 62 – 3DEC Screenshots showing dilation at 1600MN load with over 5mm interblock deformation
occurring within the maximum probable wedge .............................................................................................................................. 91
Figure 63 – ELFEN screenshot showing 3D anchor model; Principal Stress distribution on left and Total
Displacement plot on right ......................................................................................................................................................................... 92
Figure 64 – A comparison between two ELFEN models run with the same material properties but different
mesh sizes; 0.01m mesh size on left, 0.1m mesh size on right ................................................................................................. 93
Figure 65 – A Proposed Design Methodology for Analysing the Three Dimensional Cone Pullout Problem using
Discrete Fracture Networks combined with Simulations on 2D Cross Sections .................................................................. 95
Figure 66 – A Design Flow Chart indicating design inputs for various anchor design approaches ......................... 97
Figure 67 – A cumulative distribution chart showing anchor capacity variation for the rock mass generated
from numerical simulations and compared to testing data by Bruce (1976) .................................................................... 98
Figure 68 – A Flow Chart which can be used to assess whether the dead weight assumption is appropriate 101
Figure 69 – A cone pullout illustration showing to two geometric assumptions used to compare to the onset of
brittle fracturing in the ELFEN model results shown in the chart on the next figure ................................................. 102
Figure 70 – A cumulative distribution chart showing anchor capacity variation for ELFEN simulations
compared to the capacities calculated using various equivalent continuum cone strength estimates ............... 104
Figure 71 – Numerical Models Considerations Flow Chart for Design of Anchors ...................................................... 106
Figure 72 – Comparison of calibration of a 10m length fully grouted bolt with moderately dipping conjugate
jointing shown on the left and subvertical-subhorizontal jointing on the right ............................................................... 107
Figure 73 – An example of calibration of a 10m length fully grouted bolt with non-persistent, subvertical-
subhorizontal conjugate jointing and a 2.5H:1V stress ratio applied in the model ........................................................ 109
Figure 74 – An example of calibration of a 10m length fully grouted bolt with persistent, sub-horizontal jointing
and non-persistent sub-vertical jointing and a 2.5H:1V stress ratio applied in the model ........................................... 109
Figure 75 – A comparison between the dilation observed for a 10m length fully grouted cable anchor compared
to a 14m long anchor comprising a 10m bond length and a 4m free length ........................................................................ 111
Figure 76 – An example anchor test on a 17m length test anchor at the Canning Dam site. The anchor length
comprises a 10m bond length and a 7m free stressing length ................................................................................................. 112
Figure 77– A numerical simulation of the rock mass behavior for a 17m length anchor with the anchor length
comprising a 10m bond length and a 7m free stressing length ............................................................................................... 112
Figure 78– Examples of how structural interaction can be considered in anchor design ............................................. 113
Figure 79 –Relative Frequency vs Ultimate Anchor Capacity Plot for All 43 Realizations ........................................... 118
Figure 80 –Structural Domains Specific Relative Frequency vs Ultimate Anchor Capacity Plots ............................ 119
Figure 81 –ELFEN Plots overlain on failure mechanism descriptions from Wyllie ........................................................ 120
ix
ACKNOWLEDGEMENTS
The plan was simple. Surround myself with the best people I could find, give every bit of energy
toward [the project], and let the results speak for themselves. Below is a list of these people. I am
“
forever grateful for your efforts
”. - Jeremy Jones, Deeper Project.
I would like to express my sincere gratitude to my supervisor Dr. Davide Elmo for sharing his
extensive knowledge of Discrete Fracture Networks, brittle fracture mechanics and numerical
simulations with me. In addition, I would like to thank my examining committee members Dr. Erik
Eberhardt and Dr. Scott Dunbar for their useful review comments, both in the context of rock
mechanics and engineering design.
A special thank you to my good friends and mentors at Golder Associates, particularly Dr. Paul
Schlotfeldt, Mr. Richard Humphries, Dr. Jose (Joe) Carvalho and Dr. Edwin (Ted) Brown for the
reviews, encouragement and guidance both my career and in the work presented in this thesis.
I would also like to thank the British Columbia Ministry of Transportation and Infrastructure, in
particular Mr. Daryn Yonin and Mr. Terry Harbicht, for encouraging me to pursue my interest in the
field of civil engineering rock mechanics and for guidance in engineering design.
Finally, I would like to thank my fiancé Chelsie for her love and understanding in the time it took for

me to finish this thesis. I look forward to our life together and adventures that the future will bring
us in the Kootenays and the mountains of the world.
If I have seen further it is by standing on the shoulders of giants
“ ”. – Isaac Newton
x